Structural divergence, measure

There are four parameters which must be fixed to use the MLE algorithm Embedding dimension, de, maximum scale, Sm, minimum scale, Sm and evolution time, O. Basically, de is the attractor dimension where the orbits were embedded, Sm is the estimate value of the length scale on which the local structure of the attractor is not longer being proved. Sm is the length scale in which noise is expected to appear. O is fixed for compute of divergence measurements which is the necessary time to renormalize the distances between trajectories (for more details see [50]). 

The differential geometry of our constrained rolling contact demands that the contact loci cross the level curves only at points where the latter have tangents parallel to the axis. It is important to recognize that this requirement can lead to sudden disappearance of a locus. In mathematical terms the locus can suffer a "catastrophe", with an endpoint that itself has a vertical tangent. Such a catastrophic endpoint hence would manifest a diverging rate of change with temperature of the concentration of ice-like structural elements measured by... 

Measurement of the equilibrium properties near the LST is difficult because long relaxation times make it impossible to reach equilibrium flow conditions without disruption of the network structure. The fact that some of those properties diverge (e.g. zero-shear viscosity or equilibrium compliance) or equal zero (equilibrium modulus) complicates their determination even more. More promising are time-cure superposition techniques [15] which determine the exponents from the entire relaxation spectrum and not only from the diverging longest mode. 

The nitrogen atoms of the twisted amides discussed on pages 107-108 are to a greater or lesser extent pyramidal, and incipient lone pairs electron density is thus available for reactions with electrophiles. The classic example is the cage lactam [57] first prepared by Pracejus (1959), which has an amide nitrogen with near normal amine basicity. Brown and coworkers have measured rates of alkaline hydrolysis of a series of anilides [58] and [59] with related structures and find that the rate increases with increasing divergence... 

The development of mass spectroscopic techniques such as matrix assisted laser desorption (MALDI) and electrospray mass spectrometry has allowed the absolute determination of dendrimer perfection [7,8], For divergent dendrimers such as PAMAM and PPI, single flaws in the chemical structure can be measured as a function of generation to genealogically define an unreacted site of or a side reaction producing a loop at a particular generation level. Mass spectromet-ric results on dendrimers, not only demonstrate the extreme sensitivity of the technique, but also demonstrate the uniformity of the molecular mass. The polydispersity index of Mw/Mn for a G6 PAMAM dendrimer can be 1.0006 which is substantially narrower than that of living polymers of the same molecular mass [7],... 

The inclusion of the number of protons at each chemical shift proved to be key the number of false positives increased 5-7 fold (depending on how diverse the set of test compounds were) if this parameter was excluded. Various refinements were tested, but the most successful was the J Filter which disallowed a combination in which the number of couplings measured at a given chemical shift in the experimental spectrum was greater than in the predicted. This proved to be particularly valuable in the differentiation of isomers, where changes in the overall table of chemical shifts alone, could be quite subtle. The inconsistent appearance of labile protons in the experimental spectrum reduced the accuracy and it was asserted that where possible, they should be removed from both the experimental spectrum and the predicted spectrum. The mismatch level not only encoded the divergence of the experimental spectrum and the postulated structure, but also encoded... 

To investigate these problems, Brossard et al (Ref 13) analyzed data on cylindri-cally diverging detonation waves in various propane/C>2/N2 mixtures contained in divergent sectors. Detonation was initiated with an exploding wire located in the apex of the sector angle. The wave velocity was measured with ionization probes, and the wave structure was observed by means of streak-schlieren and soot-track techniques... 

It has been found out that the structure of proteins is flexible and there are many differences between the static spatial image of a protein and a dynamic view of its structure. This divergence is caused by the fact that the repetitive part of a-helices and [3-strands of protein folds, often described as a succession of secondary structures, can assume different local spatial orientation. Two experimental methods can be used to measure the flexibility in precise regions of protein structures (the anatomic mean square displacement, B-factor, measured during crystallographic experiments, and indirectly by NMR experiments which show different local conformation that could correspond directly to different stages of protein structures) (Bornot et al., 2007). 

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